Atmospheric pressure air microplasma system for true random bit generation

ABSTRACT

There is provided an atmospheric pressure air microplasma system designed for random bit generation including a plurality of plasma electrodes, a power supply module supplying a DC voltage for igniting an arc discharge between the plurality of plasma electrodes, wherein the ignited arc discharge results in establishing and sustaining an arc current channel between the plurality of plasma electrodes, a current probe for measuring and collecting electric current time series data from the arc current channel, and a data acquisition board connected to the current probe for saving the collected electric current time series data, wherein binary sequences are generated from the electric current time series data. Further, the generated binary sequences are proven to pass all 15 tests of NIST Statistical Test Suite and thereby prove to qualify as random sequences.

FIELD OF THE INVENTION

The present invention relates to the field of true random bit generationin a cryptographic system, and more particularly to a true random bitgenerator using an atmospheric pressure air microplasma system as aphysical source of entropy.

BACKGROUND OF THE INVENTION

Background description includes information that may be useful inunderstanding the present invention. It is not an admission that any ofthe information provided herein is prior art or relevant to thepresently claimed invention, or that any publication specifically orimplicitly referenced is prior art.

A microplasma is a plasma of small dimensions, ranging from tens tothousands of micrometers, and can be generated at a variety oftemperatures and pressures, existing as either thermal or non-thermalplasmas. Non-thermal microplasmas can be easily sustained andmanipulated under standard conditions, and are therefore employed invarious commercial, industrial and medical applications. Microplasmaconfined to dimensions in the order of millimeters or below are known tobe remarkably stable at high pressures. This allows self-sustained andcontinuous operation without filamentation and glow-to-arc transition.In addition, a complete microplasma system can be reduced in size, madelight-weight and in various design geometries or configurations. Whenair at atmospheric pressure is used as plasma gas (with no specializedhousing or vacuum equipment), microplasma becomes cost-effective andeasy to operate. These advantages make microplasmas ideal for portablesystems and instruments for chemical and spectrochemical analysis, thinfilm deposition, NO_(x) and SO_(x) remediation and treatment of volatileorganic compounds, biomedical decontamination, dental sterilization andmany other applications.

A majority of applications based on microplasmas rely on the fact thatmicroplasmas provide a rich environment of high-energy electrons, or anyother reactive, excited and metastable species, ultraviolet radiationsand intense electric fields without the generation of excessive heat. Inhigh-pressure and atmospheric pressure microplasmas in particular,charged and uncharged species are actually in non-local equilibrium withthe electric field due to the large and non-monotonous profiles of thelatter, and also due to the small dimensions of the system. Thisnon-equilibrium character of microplasma and erratic movement of itselements which manifests itself, for instance, as high-frequencyelectrical current fluctuations (coupled with others, such as acousticand optical fluctuations) has been shown to be useful for another typeof application, which is high-rate random bit generation (RBG). RBG isvery important in cryptographic systems, communication, Monte-Carlonumerical simulations and calculations, statistical research, randomizedalgorithms, etc.

Today's solutions to generate RBGs mostly rely either on software-basedcomputational algorithms (e.g. iterated maps or the Blum-Micalialgorithms) or on hardwired electronic circuitry (e.g. theLinear-Feedback-Shift-Registers). While these methods are cost-effectiveand relatively fast, the generated sequences are not truly random, nomatter how complex or nonlinear the systems are. Meanwhile, RBGs inHardware Security Modules (HSMs) rely on digital techniques (such asharvesting phase noise in ring oscillators, or post-processing chaoticsequences generated by a chaotic oscillator) in order to be compatiblewith the CMOS technology used for fabricating the remaining parts of thesecurity-dedicated crypto-processors. However, relying on these on-chipRBGs has its own limitations in terms of speed and vulnerability toattacks. For example, Differential Power Analysis (DPA) can be used toextract the data being processed by analyzing the current drawn by theprocessor from the chip power supply. Defenses against this class ofattacks include (for example) using random clocks or to randomly includeno operation instructions (NOP) in the device instruction stream. Suchdefenses obviously require more hardware overhead and increased designcomplexity. Chip makers use tools to simulate possible non-invasiveattacks to perform any needed improvements before a chip is fabricated.

By contrast, RBGs needed for high-speed real-time encryptionapplications mostly rely on off-chip optical sources of entropy such aschaotic lasers. Some lower speed systems also rely on harvesting noisefrom multiple sensors, including temperature, humidity, visible lightand infrared light sensors. These entropy sources have the advantage ofbeing immune to power supply attacks, but also require subsequentdigital signal post-processing platform to generate true random bits.

From the above description of traditional systems, it becomes clear thathigh-speed off-chip entropy sources needed for true RBGs (TRBGs) are upto this day mostly optical in nature. This comes with a high systemcomplexity that requires optoelectronic circuits and other optical parts(e.g. optical amplifiers, waveguides, mirrors, etc.) in order to harvestreliable signals for TRBGs. Apart from the complexity of the opticalsystems and the necessity for high precision adjustment and alignment,they still require further digital post-processing on the acquired rawbinarized data because they are only chaos based.

Accordingly, there exists a need for true high-rate RBG using a physicalsource of entropy, which overcomes the disadvantages of previously ortraditionally deployed techniques or systems.

SUMMARY OF THE INVENTION

Therefore it is an objective of the present invention to provide a TrueRandom Bit Generator (TRBG) for cryptographic systems (and other relatedapplications) using an atmospheric pressure air microplasma system as aphysical source of entropy.

The present invention involves an atmospheric pressure air microplasmasystem designed for random bit generation, comprising a plurality ofplasma electrodes, a power supply module supplying a DC voltage forigniting an arc discharge between the plurality of plasma electrodes,wherein the ignited arc discharge results in establishing and sustainingan arc current channel between the plurality of plasma electrodes, acurrent probe for measuring and collecting electrical current-timeseries data from the arc current channel; and a data acquisition boardconnected to the current probe for saving the collected electricalcurrent-time series data, wherein binary sequences are generated fromthe electrical current-time series data.

In an embodiment of the present invention, two plasma electrodes arealigned facing each other at a distance of 1 mm to 1 cm.

In an embodiment of the present invention, the two plasma electrodes aretwo needle-like electrodes.

In an embodiment of the present invention, the binary sequences aregenerated through a direct decimal-to-binary conversion of the electriccurrent time series data.

In an embodiment of the present invention, the generated binarysequences are proven to pass all 15 tests of NIST Statistical Test Suiteand thereby prove to qualify as random sequences.

In an embodiment of the present invention, the generated binarysequences qualify as random sequences without requiring post-processingof the generated binary sequences.

In an embodiment of the present invention, the atmospheric pressure airmicroplasma system is battery-powered thereby resulting in a portableand inexpensive source for true random bit generation (TRBG).

In an embodiment of the present invention, the power supply modulefurther comprises a MOSFET transistor, a step-up transformer, a diodeand an RC filter powered by a rechargeable lithium-ion battery.

In an embodiment of the present invention, the data acquisition board isfurther connected to a computer.

In an embodiment of the present invention, the arc current channel isestablished between cathodic and anodic tips of the plurality of plasmaelectrodes, through electron thermionic emission and/or field emission.

In an embodiment of the present invention, the atmospheric pressure airmicroplasma system is resilient to external power attacks.

In an embodiment of the present invention, the ignited arc discharge isvisible or non-visible with the naked eye.

As another aspect of the present invention, a true random bit generator(TRBG) using atmospheric pressure air microplasma as a source of entropyis disclosed for random bit generation in a cryptographic system, thetrue random bit generator comprising a generator switching circuit forgenerating a high-voltage microplasma between two electrodes in openair, thereby eliminating a need for optical source and components forrandom bit generation, wherein the generator switching circuit ispowered by a low voltage DC supply.

In an embodiment of the present invention, the true random bit generator(TRBG) relies on a use of current fluctuations in the atmosphericpressure air microplasma as the source of entropy for random bitgeneration.

In an embodiment of the present invention, electric current time seriesdata measured from the atmospheric pressure air microplasma is used asthe sole source of entropy for random bit generation.

In an embodiment of the present invention, the true random bit generator(TRBG) eliminates a need for digital post processing of binarized datain order to qualify bit streams as random sequences.

In an embodiment of the present invention, the atmospheric pressure airmicroplasma is generated between tip of a needle electrode and aconcentrated anolyte or catholyte of moving interface.

In an embodiment of the present invention, the true random bit generator(TRBG) further comprises a passive current sensor interfaced to acomputer via a data acquisition module.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter that is regarded as the invention is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The foregoing and other aspects, features, andadvantages of the invention are apparent from the following detaileddescription taken in conjunction with the accompanying drawings inwhich—

FIG. 1 depicts a photograph of a first prototype of a battery-poweredatmospheric pressure air microplasma system designed and investigatedfor random bit generation in accordance with the present invention.

FIG. 2 depicts a photograph of a second prototype of a battery-poweredatmospheric pressure air microplasma system designed and investigatedfor random bit generation, in accordance with the present invention.

FIG. 3 is a flow chart illustrating a complete sequence of operation inaccordance with the present invention.

FIG. 4 (a) is a graphical depiction of a typical sample of currenttime-series collected from the atmospheric pressure air microplasmasystem at a rate of 100 MS/s, in accordance with the present invention.

FIG. 4 (b) shows histogram plots for a sample of 96000 data points(arbitrarily selected from 16 MS) collected at the rates 10, 50 and 100MS/s, in accordance with the present invention.

FIG. 4 (c) depicts probability plots, in accordance with the presentinvention.

FIG. 4(d)-4(f) graphically show uniform distribution for bits ‘0’ and‘1’ wherein probability of occurrence is P (0)=P (1)=0.5 for each rate,in accordance with the present invention.

FIG. 5 shows a typical sample of current time series, in accordance withthe present invention.

DETAILED DESCRIPTION OF THE INVENTION

The aspects of the method and system to provide a true random bitgenerator (TRBG) in a cryptographic system using an atmospheric pressureair microplasma system as a physical source of entropy according to thepresent invention, will be described in conjunction with FIGS. 1-5. Inthe Detailed Description, reference is made to the accompanying figures,which form a part hereof, and in which is shown by way of illustrationspecific embodiments in which the invention may be practiced. It is tobe understood that other embodiments may be utilized, and logicalchanges may be made without departing from the scope of the presentinvention. The following detailed description, therefore, is not to betaken in a limiting sense, and the scope of the present invention isdefined by the appended claims.

A true random bit generator (TRBG) is a device that generates randombits from a physical process, rather than by means of an algorithm. Ahardware RBG typically consists of a transducer to convert some aspectof the physical phenomena to an electrical signal, an amplifier andother electronic circuitry to increase the amplitude of the randomfluctuations to a measurable level, and some type of analog-to-digitalconverter to convert the output into a digital number, often a simplebinary digit 0 or 1. By repeatedly sampling the randomly varying signal,a series of random numbers or bits is attained.

The microplasma system investigated in accordance with the presentinvention was initially generated between the tip of a needle electrodeand a concentrated anolyte or catholyte of moving interface using low DCvoltages. From the dynamic analysis of its current time series in termsof phase-space portrait, fractal dimension, largest Lyapunov exponentand power spectra, it was established that the electrochemical plasmaundergoes a transition from quasi-periodic to chaotic and hyper-chaoticbehavior as the applied voltage is increased. It was also shown that byusing larger voltages, the binary sequences generated from thecurrent-time signals unambiguously pass all needed 15 tests of NISTStatistical Test Suite and thus qualify as random sequences. However,despite these promising results, the fact that liquids and evaporatedcorrosive gases were involved in the microplasma process, posedlimitations on their portability, packaging and ease-of-maintenance.

In order to overcome some of these limitations, the present inventionrelies on the use of current fluctuations in atmospheric pressure airmicroplasma as a source of entropy for RBG. The present invention dealswith the design and testing of a high-speed TRBG system using electriccurrent time-series data measured from an atmospheric pressure airmicroplasma acting as the source of entropy. In an embodiment of thepresent invention, a stand-alone air-gap microplasma system isconsidered as a physical source of entropy for a TRBG which offers manydesirable attributes such as high-rate throughput, ease ofimplementation, and resistance to external attacks. In addition, thesystem is very cost-effective when compared to optical entropy sources,and apart from a simple binarization process, does not require anydigital post-processing on the generated bits for them to pass all 15tests in NIST Statistical Test Suite.

The proposed system is composed of a circuit powered by a low voltage DCsupply and generating a high voltage (the high-voltage value for theair-gap plasma system it is between 5 kV and 8 kV) microplasma betweentwo electrodes in open air, and a high-resolution, wide-bandwidthpassive current sensor interfaced to a computer via a high-speed dataacquisition module. The complete system is fully automated through asoftware script. After simple binarization (direct decimal to binaryconversion only) of the measured current time series data, the bitstreams pass all 15 tests under NIST 800-22 Rev. 1a Statistical TestSuite with a confidence interval of 99% without the need for anypost-processing of the binary data. This TRBG is resilient to externalpower supply attacks because the microplasma is generated at the veryhigh voltage side of the circuit. This TRBG can be used for applicationsthat require portable and high-throughput random bits such ascryptographic systems, communication systems, statistical analysis andinstrumentation.

The present invention aims to generate high-throughput and reliable truerandom bits while totally eliminating the following limitations ofcomparable traditional systems: the use of optical sources andassociated components, and the need for digital post-processing of thebinarized data in order to qualify the bit streams as random sequences.In addition, the proposed system is portable, low-cost, and operatesfrom a single battery. This is the first TRBG (to be designed and testedsuccessfully) based on using atmospheric pressure air microplasma(rather than liquid plasma) as an entropy source. The present inventionwhile maintaining high-speed and reliability requirements also does notrely on optical emissions but rather on electric current time seriesdata resulting from microplasma discharge in open air. This systemfurther generates microplasma using a simple high-voltage generatorswitching circuit powered by a low-voltage DC power supply (e.g.,rechargeable 3.7V, 2.2 Ah Li-ion battery), and provides true random bits(TRBs) without the need for post-processing (at rates that exceed 100Mbit/s, depending on the bandwidth of the current probe and samplingrate of the data acquisition module) and passes all 15 NIST standardrandomness tests with a 99% confidence.

Further, the proposed system is highly immune to possible externalattacks such as power supply attacks, due to the high-voltage requiredto create the microplasma (which is in the order of a few kVs), islight-weight and small in size which makes it portable and easy tohandle. The aforementioned features of this invention are importantconsidering that the system is solely based on electrical measurementswhich means that all associated limitations of complex optical andoptoelectronic systems are avoided, is compact in size, weight and powerconsumption (e.g. a single rechargeable 3.7V, 2.2 AH Li-ion battery issufficient to maintain operation to collect hundreds of millions of datapoints) and is successful at generating TRBs without the need for anysoftware or hardware post-processing. The throughput is limited only bythe bandwidth of the current probe and the sampling rate of the dataacquisition module.

Microplasma can be associated with strong, visible arcing or non-visiblearcing by the naked eye. The proposed invention is operational in bothconditions. However, in the case of visible arcing, high temperaturewill occur at the electrode tips and the device should not be switchedon for a long period of time (typically 5-10 seconds) which is more thanenough to collect the required data. The non-visible arcing operatingscheme is preferred because no heating effects take place and visiblelight cannot be seen with the naked eye when the plasma occurs in thiscase (no optical detection is involved in this invention). No-arcingsimply implies increasing the separation distance between themicroplasma electrodes.

FIG. 1 depicts a photograph of a typical battery-powered atmosphericpressure air microplasma system prototype designed and investigated inaccordance with the present invention. Two needle-like electrodes orplasma electrodes 102 (of 1 mm in diameter) are aligned facing eachother at a distance of about 1 mm to 1 cm. An arc discharge is ignitedand sustained in free air between the two electrodes 102 by applying ahigh voltage. The high-voltage power supply module consists of ahigh-power MOSFET transistor 104, a step-up transformer 106, a diode andan RC filter powered by a 3.5 mAh rechargeable lithium-ion battery (LIB)108. The arc current is measured using a high-frequency, highsensitivity Tektronix CT2 differential current probe 110 (1.2 kHz to 200MHz bandwidth at a sensitivity of 1 mA/mV into 50Ω) connected via aP6041 BNC probe cable or current probe output 112 to a DiligentDiscovery 2 (DD2) data acquisition board with a maximum of 100 MS/ssampling rate (this board is not part of the invention and can bereplaced by higher sampling rate boards if needed). The board isconnected via USB 2.0 to a PC for saving the collected data. The maximumcapacity of DD2's internal buffer is 16384 samples at a time.

FIG. 2 depicts a photograph of a second prototype atmospheric pressureair microplasma system designed and investigated for random bitgeneration, in accordance with the present invention. Two needle-likeelectrodes of 1 mm in diameter are aligned facing each other at adistance of about 1 mm to 1 cm, creating a plasma environment 202. Anarc discharge is ignited and sustained in free air between the twoelectrodes by applying a high voltage. The high-voltage power supplymodule consists of a high-power MOS or Bipolar transistor 204, a step-uptransformer 206, a diode and an RC filter powered by a rechargeablelithium-ion battery (LIB) 208. The arc current passing through thehigh-voltage secondary side of the transformer is measured using ahigh-frequency, high-sensitivity current probe (1 kHz to 200 MHzbandwidth at a sensitivity of 1 mA/mV into 50Ω) 210 connected to a dataacquisition board with 100 MS/s sampling rate (this board is not part ofthe invention and can be replaced by higher sampling rate boards). Theboard is connected via USB to a PC for saving the collected data. AC-language script is used to collect and save the measured currentsamples automatically and iteratively. The two prototypes in FIG. 1 andFIG. 2 serve to validate the repeatibility of the random bit generatorcircuit.

To acquire longer bit streams needed for applying the NIST tests, a Cscript was used to collect and save the 16384 samples iteratively toreach a target number of samples, as shown in the flow chart shown inFIG. 3, which illustrates the complete sequence of operation. A total of16 to 24 million samples were collected in several data batches, eachcontaining 8 million samples where the plasma is kept continuously ON.

Upon the application of a high enough DC voltage, a current channel oran arc was established between the cathodic and anodic tips of thesystem through electron thermionic emission or field emission (or bothfrom the cathode). A typical 200 μs-sample of current time-series (j₁,j₂, to j_(n)) at (t₁, t₂, to t_(n)) collected with a time resolution of32 ns from the microplasma system is shown in FIG. 4(a)—typical sampleof current time series collected from the atmospheric pressure airmicroplasma system at a rate of 10 MS/s. The signal exhibits alternatingcurrent spikes and constrictions of different durations (or differentfrequencies) and relatively low intensities superseding each wave ofhigh spikes (in the order of a few amperes) corresponding to thetransformer charging-discharges responses. This type of sustainederratic behavior was consistently observed irrespective of theorientation of the system of electrodes (i.e. horizontal, vertical, orin between) as long as a small distance of about 1 mm between the twowas maintained. An increase of this distance weakened the plasma arccurrent. The source of these current fluctuations are closely related tothe complex energy transfer processes occurring in the gas plasma, inaddition to contributions from particles (positively and negativelycharged, and neutral species) production or loss which resulted fromnumerous possible chemical reactions.

These production or loss processes are nonlinear, collision dominated,and take place with different kinetics and rate coefficients. Also,particles have different diffusion coefficients and mobilities withinthe gas medium, which makes the overall plasma state and the resultingcurrent signal in particular very difficult to predict. Thesefluctuations in current dynamics are usually linked to otherfluctuations, such as pressure, plasma speed, and optical emissions. Itshould also be noted that practically, other environmental andexperimental sources of disturbances may add up coming from air flowturbulence, temperature noise, power supply ripples, etc.

Due to this inherent complexity in microplasma systems, a fewtheoretical attempts have been carried out to explain the origin of suchfluctuations. For instance, it was traditionally demonstrated from basicgoverning equations (i.e. conservation equations of mass, momentum,energy, and metal vapor concentration, together with Maxwell'sequation), that an amplitude equation describing the temporal evolutionof perturbations of the plasma field quantities may be written as athird-order nonlinear differential equation of the form:

+μ₂ Ä+μ₁ {dot over (A)}+μ₀ A=kA³   (1)

The coefficients μ_(i) are control parameters which depend on theproperties of the generated plasma, and k is the scaling factor. Througha judicious choice of these parameters, equation (1) (also known as thejerk equation) shows that the general feature of the dynamic behavior ofindividual elements of plasma field vector may exhibit low-dimensionalchaos. Higher dimensional chaos (hyper-chaos) or more complex behaviorscannot be explained by such a model. It is also understood that even ifthe general features can be somehow depicted by such a system ofequations, which is qualitatively useful for the overall understandingof the system's behavior, the exact one-to-one matching with theexperiment is impossible to reproduce.

However, the binarized current time series collected from the presentatmospheric pressure air microplasma system are found to be random witha probability of 99% as demonstrated below. Thus, fluctuations shown byequation (1), which are at the end initiated by deterministic equations,and therefore could be eventually controlled, are inadequate to applyhere for the case of random processes. FIG. 4(b) shows histogram plotsfor a sample of 96000 data points (arbitrarily selected from 16 MS)collected at the rates 10, 50 and 100 MS/s in which the height of eachbar is the relative number of observations (i.e.,probability)—probability distribution functions of current time-seriessamples of 96000 data points collected at the rates of 10, 50 and 100MS/s, while FIG. 4(c) shows probability plots, which are nicely alignedwith the theoretical normal distribution N (μ, σ²)—normal probabilityplots of samples in (b) (dots) aligned with the theoretical normaldistribution (dashed lines), the solid thick lines connect the first andthird quartiles of the data. It was found, for instance, with aconfidence interval of 95%, the values of μ=0.81 mA and σ²=1.18 mA²(maximum variance unbiased estimator of the variance) for the samplecollected at 10 MS/s. In order to evaluate the current signal as asource of randomness, all 15 tests of the NIST Statistical Test Suitefor Random and Pseudorandom Number Generators were applied on binarizeddata. For binarization, the data were centered around the zero-mean byapplying a moving average function and removing any dc shift. Then, abase-2 representation of the absolute value of the sequence (afterscaling up by 10⁵) was generated using MATLAB function dec2bin. Finally,the binary sequence was built using the least significant bit of eachdata point.

Some statistical information on the binarized data are given in FIG.4(d)-4(f) which show uniform distribution for bits ‘0’ and ‘1’ (FIG.4(f)), and wherein probability of occurrence is P(0)=P(1)=0.5 for eachrate. (FIG. 4(d) showing bit values of a sequence of 64 successive bitsin a 1D stair plot (from the 10 MS/s current time series), FIG. 4(e)showing 2D raster image of the first 400×400 bits (generated from the 10MS/s current time series) which does not show any particularconcentration of pockets or patterns of zeros or ones and FIG. 4(f)displaying histograms of 24576000-long bit streams generated fromcurrent time series collected at 10, 50 and 100 MS/s). The number oftimes the bit ‘0’ is generated was also computed knowing that theprevious one was a ‘0’ (denoted ‘00’) and the same for ‘01’, ‘10’ and‘11’ (conditional probability P(x|y)). It was determined in a samplesize of 24576000 bits generated from the current time series collectedat the rate of 10 MS/s the respective times of occurrences of 6148108,6142061, 6142062 and 6143768. These values corresponded to theprobabilities 0.2502, 0.2499, 0.2499 and 0.2500 for ‘00’, ‘01’, ‘10’ and‘11’ respectively, meaning that there is no particular preference to anyof them and thus no form of memory of at least the prior state duringthe bit generation process. Higher-order correlation could beestablished from auto-correlation analysis.

In an embodiment of the present invention, for the execution of the NISTrandomness tests, the following parameters were used. α=0.01(significance level), block length for the Block Frequency test isM=128, block length for the Non-Overlapping Template test is m=9, blocklength for the Overlapping Template test is m=9, block length for theApproximate Entropy test is m=10, block length for the Serial test ism=16, block length for the Linear Complexity test is M=500. Table 1summarizes the statistical results from NIST randomness tests of atypical 24 M bit-long bitstream (larger than the recommended size forall NIST tests) obtained from binarized current signal, displayingtypical results of NIST tests for 24 Mbit-long bit streams generatedfrom the microplasma current time series at three sampling rates (2MS/s, 50 MS/s and 100 MS/s). The inter-electrode distance isapproximately 1 mm. The tests were performed using 50 sequences of480000 bits. The P-value, defined as the probability that a perfectrandom number generator would have produced a sequence less random thanthe tested sequence and associated with each test, is larger than α=0.01for all tests. This indicates that the sequence is considered to berandom with a confidence of 99% from the point of view of the specifictest. In the table, this is indicated by a ‘success’. If P<α, then thenull hypothesis H0 that the sequence is truly random is rejected, andtherefore it is not considered to be random, also from the point of viewof the specific test. The proportion of sequences that passed the testsfor the values of P value are also given in the table. The proportionshould be greater than p{tilde over ( )}−3√{square root over (p{tildeover ( )}(1−p{tilde over ( )})/m)}, where p{tilde over ( )}=1−α is thecomplement of the significance level and m is the sample size.Considering the present case where m=50 (most of the tests in Table 1)and α=0.01, the proportion should lie above 0.947786, which means aminimum pass rate of approximately 47/50 binary sequences.

TABLE 1 10 Mbit/s 50 Mbit/s 100 Mbit/s Statistical test P-valueProportion Result P-value Proportion Result P-value Proportion ResultFrequency 0.739928 50/50 success 0.137283 50/50 success 0.739918 49/50success Block Frequency 0.779288 50/50 success 0.911413 49/50 success0.122825 50/50 success Cumulative Sums 0.418023 50/50 success 0.21330950/50 success 0.534246 49/50 success Runs 0.202219 49/50 success0.779188 50/50 success 0.023545 49/50 success Longest Run 0.383827 50/50success 0.13681  47/50 success 0.035716 50/50 success Rank 0.38382750/50 success 0.455937 50/50 success 0.816537 50/50 success FFT 0.41902150/50 success 0.122325 48/50 success 0.657933 49/50 success NonOverlapping Template 0.383827 47/50 success 0.419021 50/50 success0.616395 48/50 success Overlapping Template 0.935718 49/50 success0.739918 49/50 success 0.191887 50/50 success Universal 0.739918 50/50success 0.574903 50/50 success 0.419021 50/50 success ApproximateEntropy 0.883171 49/50 success 0.066882 49/50 success 0.289007 50/50success Random Excursions 0.002071 15/15 success 0.634308 26/26 success0.911413 22/22 success Random Excursions Variant 0.437274 15/15 success0.01265  26/26 success 0.123325 22/22 success Serial 0.262240 49/50success 0.657933 49/50 success 0.770188 48/20 success Linear Complexity0.23681  49/50 success 0.383827 47/50 success 0.699313 50/50 success

The performance of the microplasma system was also tested at higherrates for RBG, which is useful not only for increasing the throughputbut also for limiting the ON time of plasma system and hence increasingits lifetime. In particular, the system with 50 MS/s and 100 MS/ssampling rates was tested. Some statistical information on the currenttime series and binarized data obtained at these two rates are shown inFIGS. 4(b), (c) and (f). The corresponding results for NIST tests arereported in Table 1, which confirm the randomness of the generated bitstreams up to 100 MS/s sampling rate. This sampling rate is the limit ofthe used hardware data acquisition system. Nonetheless, at this samplingrate, the time taken to collect all 16 M data points was just 3.3seconds, in addition to approximately 2.0 seconds needed by the relay toswitch the plasma ON and get it stabilized.

Finally, in order to see how the NIST tests of randomness are affectedif the inter-electrode distance is increased, the scenario wherein thetwo electrodes were pulled apart to about 2 cm was considered. At thisseparation distance, an acoustic signal emanating from the microplasmaenvironment could be heard but no visible optical emissions wereobserved with the naked eye. In spite of that, the resulting currenttime series still appeared to be intermittent and disorganized as shownin FIG. 5. The NIST tests conducted on the binarized data following thesame procedure aforementioned were all passed (with P>α=0.01 andproportion pass rate larger than the minimum) as shown in Table 2. Thisdemonstrates that the inter-electrode distance has, to a certain extent,little effect on the RBG performance of our atmospheric pressure airmicroplasma system. In addition, because the high current spikesobserved when visible arc plasma was in place are considerably reduced,this in turn reduces the degradative effects of electrodes over-heating.

TABLE 2 2 Mbit/s 50 Mbit/s 10 Mbit/s Statistical test P-value ProportionResult P-value Proportion Result P-value Proportion Result Frequency0.002043  99/100 success 0.798139  98/100 success 0.574903  98/100success Block Frequency 0.366918  99/100 success 0.554420 100/100success 0.816537  99/100 success Cumulative Sums 0.236810  99/100success 0.595549  99/100 success 0.401199  98/100 success Runs 0.867692 99/100 success 0.401199 100/100 success 0.055361  99/100 successLongest Run 0.012850  99/100 success 0.096578 100/100 success 0.999438 99/100 success Rank 0.289667  99/100 success 0.319084  99/100 success0.834308 100/100 success FFT 0.236810  97/100 success 0.236810  99/100success 0.236810 100/100 success Non Overlapping Template 0.0055361 96/100 success 0.5341416  99/100 success 0.891163  99/100 successOverlapping Template 0.455937  98/100 success 0.319084 100/100 success0.616305 100/100 success Universal 0.534146 10/10 success 0.739918 10/10success 0.213309 10/10 success Approximate Entropy 0.946308 100/100success 0.085587 100/100 success 0.224821 100/100 success RandomExcursions 0.350485 16/16 success 0.275709 22/22 success 0.012650 15/15success Random Excursions Variant 0.035174 16/16 success 0.739918 21/22success 0.275709 15/15 success Serial 0.574903 100/100 success 0.897763 99/100 success 0.935716  99/100 success Linear Complexity 0.455937 99/100 success 0.153763  99/100 success 0.616305 100/100 success

The use of a battery-powered atmospheric pressure air microplasma systemwas demonstrated as a portable and inexpensive source for high-rateTRBs. The inherently unpredictable nature of the microplasma currenttime series was relied on as a source of entropy. The generatedsequences at rates up to 100 Mbit/s successfully passed all 15statistical tests under NIST 800-22 Rev. 1a with a confidence of 99%.However, for extended longevity and reliability of the device, it isrecommended to monitor the degradative electrode erosion effect whichresults from particle bombardment and associated local heating. Theseeffects were minimized by limiting the plasma ON time to a few seconds,and/or by increasing the inter-electrode separation to limit the plasmacurrent. Even so, all 15 NIST tests were passed successfully withP-values>0.01 and proportions pass rate larger than the minimum.

In another embodiment, the associated optical and acoustic signals ofthe atmospheric pressure air microplasma system also generate high-ratefluctuations that need to be investigated using non-linear time seriesanalysis and statistical tests for randomness. Furthermore, preliminarytests have shown that the binarization procedure can be completelyavoided while using directly the bits generated by the samplinganalog-to-digital converter in the data acquisition module.

Many changes, modifications, variations and other uses and applicationsof the subject invention will become apparent to those skilled in theart after considering this specification and the accompanying drawings,which disclose the preferred embodiments thereof. All such changes,modifications, variations and other uses and applications, which do notdepart from the spirit and scope of the invention, are deemed to becovered by the invention, which is to be limited only by the claimswhich follow.

The invention claimed is:
 1. An atmospheric pressure air gap microplasmasystem designed for random bit generation, comprising: a plurality ofplasma electrodes; a dc power supply module supplying a voltage forigniting an arc discharge between the plurality of plasma electrodes,wherein the ignited arc discharge results in establishing and sustainingan electric current channel between the plurality of plasma electrodes;a passive current probe for measuring and collecting electric currenttime series data of the electric current channel; and a data acquisitionboard connected to the current probe for saving the collected electriccurrent time series data, wherein binary sequences are generated fromthe electric current time series data.
 2. The atmospheric pressure airgap microplasma system of claim 1, wherein two plasma electrodes arealigned facing each other at a distance of 1 mm to 1 cm.
 3. Theatmospheric pressure air gap microplasma system of claim 2, wherein thetwo plasma electrodes are two needle-like electrodes.
 4. The atmosphericpressure air gap microplasma system of claim 1, wherein the binarysequences are generated through a direct decimal-to-binaryconversion ofthe electric current time series data.
 5. The atmospheric pressure airgap microplasma system of claim 1, wherein the generated binarysequences are proved to pass all 15 tests of NIST Statistical Test SuiteSP 800-22 and are thereby suitable for random bit generatorapplications.
 6. The atmospheric pressure air gap microplasma system ofclaim 5, wherein the generated binary sequences are suitable for randombit generator applications without requiring post-processing of thegenerated binary sequences.
 7. The atmospheric pressure air gapmicroplasma system of claim 1, wherein the atmospheric pressure air gapmicroplasma system is battery-powered thereby resulting in a portableand inexpensive source for true random bit generation (TRBG).
 8. Theatmospheric pressure air gap microplasma system of claim 1, wherein theatmospheric pressure air gap microplasma system further comprises aMOSFET transistor, a step-up transformer, a diode and an RC filterpowered by a rechargeable lithium-ion battery.
 9. The atmosphericpressure air gap microplasma system of claim 1, wherein the dataacquisition board is further connected to a computer.
 10. Theatmospheric pressure air gap microplasma system of claim 1, wherein thearc current channel is established between tips of the plurality ofplasma electrodes, through electron thermionic emission and/or fieldemission.
 11. The atmospheric pressure air gap microplasma system ofclaim 1, wherein the atmospheric pressure air gap microplasma system isresilient to external power attacks.
 12. The atmospheric pressure airgap microplasma system of claim 1 for random bit generation, wherein theignited arc discharge is visible or non-visible with the naked eye. 13.A true random bit generator (TRBG) using atmospheric pressure air gapmicroplasma as a source of entropy for random bit generation, the truerandom bit generator comprising: a generator switching circuit forgenerating a high-voltage microplasma between two electrodes in openair, thereby eliminating a need for optical source and components forrandom bit generation by establishing and sustaining an electric currentchannel between the two electrodes, wherein the generator switchingcircuit is powered by a long voltage DC supply.
 14. The true random bitgenerator (TRBG) of claim 13, wherein the true random bit generator(TRBG) relies on a use of current fluctuations in the atmosphericpressure air gap microplasma as the source of entropy for random bitgeneration.
 15. The true random bit generator (TRBG) of claim 13,wherein electric current time series data measured from the atmosphericpressure air gap microplasma is used as the sole source of entropy forrandom bit generation.
 16. The true random bit generator (TRBG) of claim13, wherein the true random bit generator (TRBG) eliminates a need fordigital post-processing of binarized data in order to qualify bitstreams for random bit generator applications.
 17. The true random bitgenerator (TRBG) of claim 13, wherein the true random bit generator(TRBG) further comprises a passive current sensor interfaced to acomputer via a data acquisition module.